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Appendix VI.

polygon, and join lines to corners. Commencing at any point on
A draw the polygonal lines shewn in space diagram parallel to the
radials in vector figure and in order, and letter as shewn. These
lines are known as the links, and are lettered according to Bow's
method. O c^ and 0 5X are the first and last links respectively,
and at their intersection x is placed the resultant force line R,
parallel to 05. The proof is very simple. Imagine the space
polygon to be a framed structure or endless string held taut by

the original forces. Every corner of this string has three forces,
as for example Oji i1O Ool: and these have the force
diagram O o i^. It follows that the whole of the vector figure is
the force diagram for the framed structure, and if R'S direction be
reversed all the forces are in balance.

Two particular cases occur: (i) When the vector figure only
is closed, o falling on 5, the resultant is a couple whose forces are
each equal to O o or O 5, and whose area will be found from the
space diagram; (2) when both polygons close, the resultant is
zero, the forces being already balanced.